Aside from anything else it's lost the taxpayer billions
I doubt that is the net effect.
Thousands of people moved (who might not have done so otherwise) , and the bottom of the chain feeds the top, so enabling many purchases that were above the holiday threshold and invoke the highest levels of tax on huge sums.
Also the busy property market kept thousands of businesses in business: EAs, solicitors, surveyors (regular, damp, structural etc), removals companies, tradespeople. Businesses that pay tax, for services that earn VAT for the Gvt.
All these individuals were kept from claiming furlough. All paid tax on their earnings.
I paid more than 6 months of my salary to EAs, solicitors, surveyors, cleaning and small
Jobs people, removal co, and an extra 20% to the Gvt. And all
Those people paid tax on what I paid them.
The SDLT holiday for the middle of the market (FTB and high cost homes not affected) was a ‘lost leader’ in supermarket terms. The property market is worth billions to the Gvt with or without SDLT.